Problem: Emily is 2 times as old as Luis. Sixteen years ago, Emily was 6 times as old as Luis. How old is Luis now?
Solution: We can use the given information to write down two equations that describe the ages of Emily and Luis. Let Emily's current age be $e$ and Luis's current age be $l$ The information in the first sentence can be expressed in the following equation: $e = 2l$ Sixteen years ago, Emily was $e - 16$ years old, and Luis was $l - 16$ years old. The information in the second sentence can be expressed in the following equation: $e - 16 = 6(l - 16)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $l$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = 2l$ . Substituting this into our second equation, we get: $2l$ $-$ $16 = 6(l - 16)$ which combines the information about $l$ from both of our original equations. Simplifying the right side of this equation, we get: $2 l - 16 = 6 l - 96$ Solving for $l$ , we get: $4 l = 80.$ $l = 20$.